How many concessions can a city ask for, anyway? Boston pushes developers of residential and mixed-use projects for lots of things, including environmental sustainability, thoughtful street-level planning, and a smattering of below-market-rate housing units. Frustrated by a succession of boring glass boxes, Mayor Marty Walsh has called for one more: adventurous architecture.

In practice, all these things cost money, and even deep-pocketed developers make choices. That’s especially evident as the city tries to sell off a decrepit garage in Winthrop Square. Earlier this month, each of six development teams presented its ideas in an open house at Faneuil Hall. On Monday, the Boston Redevelopment Authority revealed each team’s bid for the garage. A team that splurges on housing affordability or snazzy architectural moves has less money to spend to buy the property itself.

The trade-offs are stark.

Accordia Partners

Payment to city: $50 million

Rough concept: “Beauty, but It’ll Cost You”

This residential and hotel project would pay the city the smallest sum but offers the greatest rewards to anyone who’d actually have to look at the building every day. The exterior incorporates terra cotta in addition to the usual glass, and its unusual profile changes dramatically from one vantage point in the city to the next. Designing the building to LEED platinum environmental standards adds expense, too. The number of new housing units is modest — about 185 condos, plus support for 125 below-market units off-site. Still, if Walsh and his BRA want a daring new addition to Boston’s skyline, this plan is it.

HYM Investment Group

(The HYM Investment Group, LLC)

Payment to city: $68.3 million, plus $31.8 million for a public school

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Rough concept: “Divine Inspiration”

In a twist, this team would put its tower on an Arch Street site now occupied by St. Anthony Shrine and build a new shrine, along with a public school, on the city’s Winthrop Square land. At a recent Faneuil Hall open house featuring all six proposals for Winthrop Square, HYM even had a friar on hand — a sales pitch that harks back to a more instinctively Catholic Boston. The project is farsighted in one key way: Downtown will need a school as it attracts more residents. What HYM won’t do is broaden the design conversation in Boston. The plans come from the prolific Elkus Manfredi Architects, the default firm of risk-minimizing developers in Boston.

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Lendlease Development Inc. et al.

Payment to city: $75 million

Rough concept: “Stand Out in a Crowd”

Meanwhile, the project by Lendlease, Hudson Group North America LLC, and Eagle Development Partners takes up Walsh’s call for more boldness, and then some. The diagonal lines wrapping around much of the tower are meant to reference the irregular street map of Boston’s old downtown; the grid pattern elsewhere on the building supposedly evokes the Back Bay. Give the team credit for moving beyond the standard shiny box, but this is a swing and a miss — the local equivalent of a Shanghai skyscraper that looks dated as soon as it’s complete.

Millennium Partners

Payment to city: $150.8 million (subject to conditions)

Rough concept: “Show You the Money”

No other developer showed up at the Faneuil Hall event with a virtual-reality viewer to promote its signature feature — in Millennium’s case, a soaring lobby called the Great Hall. The company is also promoting something more important: a reputation for getting big projects finished. It was Millennium that Tom Menino tapped to turn an embarrassing pit at Downtown Crossing into an attractive mixed-use complex. The company also made the most generous offer for the Winthrop Square site: $100 million, plus $100 for every square foot of saleable residential space. That price structure discourages the city from shrinking the project if wind- and shadow-phobes object to its size. Shrewd.

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Trans National Properties

(Trans National Properties)

Payment to city: $75 million

Rough concept: “The Bigger, the Better”

This team controls the land next to the Winthrop Square garage. Combining the two sites would create room for two towers, vast office spaces, and hundreds of residential units. In some ways, Trans National’s proposal encapsulates a changing economy; it’s among the proposals that include a startup accelerator, and the developer’s residential partner is Toll Brothers, the suburban homebuilder that’s now chasing millennials and empty nesters into urban cores. On the downside: Trans National would remove a cool building by Paul Rudolph, a polarizing but influential architect. Too bad — the building is worth saving.

Trinity Financial

(Trinity Financial, Inc.)

Payment to city: $60.5 million

Rough concept: “Follow Your Heart”

This project makes the most direct appeal to the conscience of a liberal city amid yawning economic inequality. Besides a hotel, it includes about 650 residential units and would reserve 40 percent of them for middle-class families. The numbers still have to work out. Trinity’s bid for the garage falls on the low side, and the project’s overall design is generic. Even so, a shortlist that includes Trinity, along with design standout Accordia and high bidder Millennium, would present Bostonians with a crisp choice. A strong emphasis on below-market housing, architectural interest, or maximum value for the garage? Pick, because we can’t have all three.